Generation of topologically complex three-dimensional electron beams in a plasma photocathode

Laser-triggered ionization injection is a promising way of generating controllable high-quality electrons in plasma-based acceleration. We show that ionization injection of electrons into a fully nonlinear plasma wave wake using a laser pulse comprising of one or more Laguerre-Gaussian modes with combinations of spin and orbital angular momentum can generate exotic three-dimensional spatial distributions of high-quality relativistic electrons. The phase dependent residual momenta and initial positions of the ionized electrons are encoded into their final phase space distributions, leading to complex spatiotemporal structures. The structures are formed as a result of the transverse (betatron) and longitudinal (phase slippage and energy gain) dynamics of the electrons in the wake immediately after the electrons are injected. Theoretical analysis and three-dimensional simulations verify this mapping process leads to the generation of these complex topological beams. These beams may trigger novel beam-plasma interactions as well as produce coherent radiation with orbital angular momentum when sent through a resonant undulator.

Figure 1

The structures of the injected electrons at ${\omega }_{p}t=31$. First row: Isosurface of the electron density and its projections on each plane. Second row: Normalized density distribution of the electrons in the $\theta -\xi$ plane. The black dashed lines represent the predications from Eq. (2). Third row: bunching factor.

Figure 2

Theoretical analysis of the twisted structure. (a) $g_{2,1}(\theta )$ with $k_p{\xi }_i=2.24$. The value at each $\alpha$ is normalized by 10 when $1\le |\alpha |<2$ and its maximum for other $\alpha$. (b) The bunching factor ($k=0,l_b=l+\sigma$) and the betatron phase of the electrons ionized with $k_p{r}_i=0.1,a_i=0.1,k_p{\xi }_i=2.24$, and $t_i=0$. (c) $l=0$, $\sigma =1$: the distribution of the electrons and their centers (black circles) at ${\omega }_{p}t=31$ in five different slices using Eq. (1). (d) The evolution of the peak of the bunching factor and the radial position of the center of the $k_p\xi =3$ slice.

Figure 3

The structure of the injected electrons when two right-handed $CP$ laser pulses with $(l=0,p=0)$ and $(l=2,p=0)$ are used. (a) A illustration of the laser-triggered ionization injection in a beam driven plasma wake. (b) Density isosurface and its projections to each plane. (c) The bunching factor. The profiles of the pulses are as same as in Fig. 1.

Figure 4

The structures of the injected electrons at ${\omega }_{p}t=31$ when a $CP$ laser pulse with $(\sigma =-1,l=0,p=0)$ or $(\sigma =-1,l=2,p=0)$ is used. The first column: the isosurface of the electron density distribution and its projections on each plane. The second column: the bunching factor of the injected electrons.

Figure 5

Longitudinal phase space of the injected beams at ${\omega }_{p}t=31$. The charge density is normalized to its peak in each subplot. The black lines are the energy spectrum. The blue line in the self-consistent case (bottom right) shows the current profile.

Figure 6

Simulation study of the conservation of ${\overrightarrow{P}}_{\perp }$. The profile and intensity of the laser pulse is the same as that of Fig. 1.

Figure 7

The direction of the transverse momentum of 1000 sampled electrons.

Figure 8

The value of $g_{l,\sigma }(\overline{x})$. Note the value at each $\alpha$ is normalized by 10 when $1\le |\alpha |<l$ and its maximum for other $\alpha$.

Figure 9

Left: the initial distribution of the electrons. These electrons are initialized with $k_p{r}_i=0.1,a_i=0.1,k_p{\xi }_i=2.24$ and $t_i=0$. Right: the evolution of $\theta$ and the betatron phase $\mathrm{\Phi }$.